(untitled) (Journal of Computational Mathematics, 2002)
This paper is mainly concerned with solving the following two problems: Problem I. Given X C^n × m , Λ = diag( λ_1, λ_2, …, λ_m) C^m× m. Find A ABSR^n × n such that AX=XΛwhere ABSR^n × n is the set of all real n× n anti-bisymmetric matrices. Problem Ⅱ. Given A^* R^n × n. Find A S_E such that ||A^* - A||_F=AS_E||A^*- A ||_F,where ||·||_F is Frobenius norm, and S_E denotes the solution set of Problem Ⅰ. The necessary and sufficient conditions for the solvability of Problem Ⅰ have been studied. The general form of S_E has been given. For Problem Ⅱ the expression of the solution has been provided.